The ICC has cleared opposing captains Virat Kohli and Steve Smith, plus a number of other players who were involved in run-ins or send-offs during the tense clash.
"We would encourage both teams to focus their energies on the third Test in Ranchi next week. Ahead of that, the match referee will bring both captains together to remind them of their responsibilities to the game," ICC chief executive David Richardson said in a statement.
Virat Kohli Photo: Photosport
Kohli accused Smith of 'crossing the line' when he was given out leg before wicket but looked towards the players' area in the stands as he mulled over whether to ask for a review of the umpire's decision using DRS.
Players are not allowed to seek direction on reviews apart from conferring with the non-striker. Neither team can make more than two unsuccessful review requests per 80 overs.
Smith said it was a one-off incident caused by "brain fade" but Kohli countered that it was not the first time it had happened and that he had complained to the match officials.
Australia captain Steve Smith Photo: Photosport
"In relation to Steve Smith and Virat Kohli, the ICC has considered both incidents in the context of this match and concluded it will be taking no further action against either player," the governing body said in a statement.
The third test between the teams starts in Ranchi on March 16 with the series level at 1-1.
"Ahead of (the third test), the match referee will bring both captains together to remind them of their responsibilities to the game," Richardson said.
Australia coach Darren Lehmann and Cricket Australia chief executive James Sutherland have vehemently rejected Kohli's allegations of systematic cheating.
"I find the allegations questioning the integrity of Steve Smith, the Australian team and the dressing room, outrageous," Sutherland said.
"We have every faith that there was no ill-intent in his (Smith's) actions.
"We reject any commentary that suggests our integrity was brought into disrepute or that systemic unfair tactics are used."
Kohli could yet be booked for his tirade. David Warner was fined for "public criticism of, or inappropriate comment" in 2014, when he accused AB de Villiers of ball-tampering in a radio interview.
Relations between the sides have soured following the acrimonious postscript to the hosts' 75-run win that levelled the four-Test series.
Not since the 'monekygate' saga of 2008 has there been so much spite on and off the field in a Border-Gavaskar battle.
Former India skippers Sourav Ganguly, Sunil Gavaskar and Kapil Dev had called on the ICC to investigate Australia, while Smith's predecessor Michael Clarke suggested there may be some merit to Kohli's sensational claim.
Sutherland is set to have pre-planned meetings with BCCI officals later this week.
A contrite Smith called his misdeed a one-off brain fade, while coach Lehmann was "very surprised" to hear Kohli's allegations.
"Never, ever, ever," Lehmann said, when asked if he or other support staff have communicated with players regarding whether to review.
"He has his opinion and we have ours.
"We've never done any of that."
Lehmann has fired back at many antagonists in the past - be it as a player or coach.
But on this occasion he adopted a non-confrontational approach, also praising his charges for not matching Kohli's in-your-face aggression.
Darren Lehmann, Australia coach. Photo: Photosport
"Gone are the days when we used to be probably the other way, and I was part of that as an Australian side," Lehmann said.
"We've changed the way we want to play.
"I'm pretty pleased with the way we do things now ... I'm really proud."
However, Josh Hazlewood, Mitchell Starc and Steve O'Keefe all gave Indian batsmen send-offs during the intense clash.
